"Semitonal" JI structures; some interesting sounds for you

I've been experimented a lot with constructing sonorities of
intermediate tonalness; sonorities that on one hand sound like they
should resolve one way, but then don't. Perhaps "semitonal" is a good
word for these types of structures. "Quasi-rooted" triads are an
interesting class of these sonorities. A triad like 10:12:15 is
quasi-rooted; it sounds like it refers to 5 more 1. These triads tend
to resolve to a certain note, but don't really fully "make sense," or
resolve fully; they're a bit higher in entropy and I believe related
to the perception of "minorness." At the very least they sound really
complex and interesting.

An abstract extension of the concept of the quasi-rooted triad, and a
technique that generates loads of semi-tonal sounds right off the bat,
is to use the harmonic series as a patchwork quilt. You start with a
structure, take a chunk out of it, and replace it with another chunk
that has the same outer dyad. I'll give you an example:

- Start with 2:4:6:8:9:10:11:12.
- Now take that 8:9:10:11:12 chunk - see how the outer dyad is a 3/2?
- Now replace that chunk with another chunk of the harmonic series in
which the outer dyad is also a 3/2.
- Let's try the following options: 6:7:8:9, 10:11:12:13:14:15,
14:16:17:19:21, 18:20:22:24:27. Pop the 8:9:10:11:12 out and snap
these pieces in there instead.
- This leads to the following chords: 3:6:9:12:14:16:18,
5:10:15:20:22:24:26:28:30, 7:14:21:28:32:34:38:42, and
9:18:27:36:40:44:48:54.
- Note the very subtle difference between second and third one.
- If you tend to hate cluster chords and don't like critical band
effects, feel free to take subsets of the above chords.

Those sounded fairly familiar, so here's a more xenharmonic example:
- Start with 2:4:6:7:8
- Check out the 6:7:8, note that it has an outer dyad of 4/3.
- Now pop that 6:7:8 out and give it a 9:10:11:12 transplant. Try
12:13:15:16 too. Try 21:23:25:28 and 21:23:26:28 too.
- This gives you 3:6:9:10:11:12, 4:8:12:13:14:15:16 (this one is
actually rooted, can you hear the difference?), 7:14:21:23:25:28, and
7:14:21:23:26:28.

Some interesting neutral sounds here. Can we make "sad" sounds? Let's
see if we can't create a "minor" sounding chord that actually is as
sad as 5-limit minor:
- Start with 2:4:7:8:9:11.
- Go back to the original chord, and this time replace the 7:8:9:11
with 14:16:19:22. This is 4:8:14:16:19:22. I flip that 19 back and
forth from 18 and hear major, minor, major, minor.
- Go back to the original chord, and this time replace the 7:8:9:11
with 14:17:18:20:22. This is 4:8:14:16:17:19:22. A bit less restful.
- Go back to the original chord, and this time replace the 7:8:9:11
with 504:576:693:792. This is the utonal inverse of 7:9:11, with the 8
left alone. This is 144:288:504:576:616:792. To me this sounds pretty
dissonant.
- Go back to the original chord, and this time replace the 7:8:9:11
with 504:616:693:792. This is utonal inverse of 7:8:9:11 in which 8 is
flipped upside down as well. This is 144:288:504:616:693:792. Still
sounds somewhat minor to me. It's interesting to compare this to
4:8:14:16:19:22 and see how they relate.

I find these sounds very interesting. They produce xenharmonic "minor"
chords, in an abstract sense, as is 4:7:9:11 a xenharmonic "major"
chord. They differ in "minorness" and some are more sad-sounding than
others. There are probably ways to create chords that feel similar
that don't involve this particular "patchwork" approach as well.

In this sense, both 10:15:20:24:30 and 10:15:20:26:30 can be thought
of as semitonal sonorities that build off of 2:3:4:6, where the 4:6 is
replaced with 10:12:15 and 10:13:15. The 2:3:4:6 resolves to one VF,
and the 10:12:15 and 10:13:15 don't fit perfectly into that. Of the
two, 10:12:15 sounds more "minor" to me. This could be because it's
higher in entropy, or because it's also the utonal version of 4:5:6.
You decide.

-Mike